Carleson box
= Carleson box
{c}
{title2=$S(I)=\{r\xi:\xi\in I,\ 1-m(I)<r<1\}$}
A boundary neighborhood over an arc $I$ of the <unit circle>, with radial depth equal to its normalized angular length $m(I)$. Changing that depth by any fixed positive factor gives an equivalent <Carleson measure> condition. Large arcs and central mass can be handled separately by finitely many fixed neighborhoods covering the <unit disc>.